Straight Line Geometric Path Lengths – Examples and Distributions

Abstract

The straight line geometric path distribution of different shapes is a fundamental parameter of any a detector sensitive and in the presence of high energy charged particles such as galactic cosmic rays (GCRs). Knowledge of the straight line path distribution can yield first estimates of the expected energy distribution due to minimum ionizing particles. This predicted shape provides a valuable interpretation tool of spectra of particles that are unlikely to stop in a detector and may present a background or desired signal. These quantities have been calculated many times before including analytically, Coleman (1973), and even in Geant4 software, (Agostinelli, Allison et al. 2003, Santin, Ivanchenko et al. 2005). For this work we utilize the Rapid Adaptable Multi-threaded Particle and Radiation Transport (RAMPART) simulation framework and collect some common shapes all with the same volume to serve as a reference of path lengths and instructions manual for computing other shapes as desired.